Philip W. Anderson, a More as Well as Different Physicist

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Any graduate student ploughing through a course on quantum field theory will doubtless learn about spontaneous symmetry breaking – an elegant and ubiquitous mechanism in the study of theoretical physics that, most famously, clarifies the crucial role the recently discovered Higgs boson plays in elementary particle physics. And the student will note, often with incredulity, the fact that it was not a high-energy physicist but an exponent of a different field, called condensed matter physics, named Philip W. Anderson who was the first to elucidate its mechanism in a crisp note published two years before Peter Higgs and others published their famous symmetry-breaking papers in 1964.

The Nobel Prize for predicting the Higgs boson and explaining the role it plays in the study of fundamental particles was eventually awarded to Higgs and François Englert in 2013, but not to Anderson, however.

Such prescience characterises much of Anderson’s work in solid-state and condensed matter physics, to which he made numerous and wide-ranging contributions. Anderson passed away at the age of 96 on March 29, in Princeton, New Jersey.

Anderson was ever the keen observer not only of various developments in his fields of interest but also of his own intellectual trajectory. He in fact noted as much and preferred to call his observations premature instead. It is silly to think one can do justice to the influence Anderson has had on the development of condensed matter theory in a short article, and no doubt in the days to come, more competent physicists will share with us their memories of Anderson’s genius.

Localisation

A recurring motif in Anderson’s work is the exploration of novel emergent structures. Consider the theory describing the electron, first advanced by the British physicist Paul A.M. Dirac in 1932. Dirac wrote that with this theory, “the principles underlying much of physics and all of chemistry” had been determined. That is, Dirac’s theory of the electron, coupled with some facts about the way electric and magnetic forces behave, are in principle sufficient to explain pretty much all of chemistry. So with all the basic rules in place governing ions, electrons, and their electromagnetic interactions, what further mysteries could subjects like solid-state physics possibly hold?

It’s not too hard to come up with a simple example, let alone more exotic ones. Consider the humble copper wire: it is shiny, ductile and cool to touch. These are simple properties of metals that we learn in school, but we know that it is absurd to think these same properties – lustre and ductility, for example – are exhibited by the copper atoms that make up the wire. What makes metals metallic in this sense isn’t some quantum of ‘metallicity’ that the copper atoms carry. Instead, metallicity is an emergent property that arises from multiple copper atoms interacting with each other – in the same way that while salt crystals are cubic, these cubic crystals aren’t made of tiny cubic molecules of salt.

Let’s return to the question of conductivity. According to Paul Drude’s classical theory of electrical conductivity, metals – which are made up of ionic lattices and swarms of electrons crowding and otherwise darting back and forth – conducted electricity because electrons moved through the lattices while carrying electric charge. The further an electron could get without bumping into an ion, or another electron, the better the metal would conduct. This distance, called the mean (average) free path, could be measured. But when scientists did, they found it to be orders of magnitude larger than the average distance between the ions that made up the lattice. How did the electrons manage to travel hundreds of lattice units without knocking into a single ion?

The answer to this conundrum came from quantum theory, which replaced this Drude’s classical model with a more fluid, wavy description of the electrons. Since electrons exhibited wave-like properties, as quantum theory taught us, the electrons would really diffract within an ideal crystal, and experience resistance only when the crystal structure had imperfections like dislocations or impurities. That is, the electron bounds from impurity to impurity, so the more impure the crystal is, the shorter the mean free path, and thus lower the conductivity.

That was before Anderson arrived on the scene.

Anderson asked himself if this picture would always be true or if something more drastic might happen along the way, as he imagined making the lattice more and more imperfect. He found that after a critical degree of imperfection, the electron’s ability to conduct electricity did not just diminish – it vanished altogether, with the electrons nearly completely immobilised by the disorderly lattice around them. This is called Anderson localisation. By tuning the imperfections in the lattice, we can induce a transition from metallic behaviour to insulating behaviour!

For these investigations into the behaviour of disordered and magnetic systems, Anderson was awarded the Nobel Prize for physics in 1977, along with Nevill Mott and J.H. Van Vleck.

Emergence

While Anderson’s influence is felt perhaps most by those physicists working in condensed matter physics, he is better known among a wider community of scientists and philosophers for an article entitled ‘More Is Different‘, published in Science in 1972. He was responding in part to a parade of popular science books by eminent (high-energy) physicists waxing lyrical about the successes of the reductionist philosophy: that there were a set of “fundamental” laws and that once they were figured out, everything else was just a matter of computational ability. Anderson thought this idea was widespread and pernicious, and had to be beaten back. The reductionist view really dates to Pierre-Simon Laplace, who wrote confidently in 1820:

An intelligence knowing all the forces acting in nature at a given instant, as well as the momentary positions of all things in the universe, would be able to comprehend the motions of the largest bodies as well as the lightest atoms in the world, provided that its intellect were sufficiently powerful to subject all data to analysis; to it nothing would be uncertain, the future as well as the past would be present to its eyes…

Railing against Laplacian determinism, Anderson argued that new scales and degrees of complexity bring with them their own concepts, principles and laws that cannot be derived by straightforward extrapolation from their simpler pieces. That is, there is no “fundamental” branch of science. Rather, each scale requires its own fundamental principles, with the fields they define arranged hierarchically according to the idea that “The elementary entities of science X obey the laws of science Y.”

Anderson was quick to add that the composite entities of science X may require the introduction of new concepts altogether. For example, the notion of metallicity is not built into the elementary constituents of solid-state physics, i.e. atoms. Instead, it is an emergent property that emerges from the collective behaviour of multiple atoms together. Anderson summarises this very simply:

The important lessons to be drawn are two: 1) totally new physics can emerge when systems get large enough to break the symmetries of the underlying laws; 2) by construction, if you like, those emergent properties can be completely unexpected and intellectually independent of the underlying laws, and have no referent in them.

What excited Anderson about this image of the sciences is that it required “the idea of intellectual autonomy of the two [different] levels of understanding”, careful not to relegate any science to a secondary, less important role. “Psychology is not applied biology, nor is biology applied chemistry.” Anderson’s later interest in the then-emerging field of complex systems essentially continued from this worldview.

In responding to an op-ed by Marvin Goldberger and Wolfgang Panofsky in the New York Times, characterising branches of physics other than particle physics as merely an application of the fundamental laws of nature, Anderson asked, “If broken symmetry, localisation, fractals and strange attractors are not ‘fundamental’, what are they?”

This view of science Anderson so patiently articulated across decades is almost magical. While books by Abraham Pais, Steven Weinberg and Stephen Hawking exhorted us to look deep into the vanishingly small, Anderson taught us to widen our gaze and to look up into the seemingly infinite hierarchy of sciences. He wrote many scientists worry that “by accepting the close relationships among all the sciences, they will somehow become the slaves of determinism and of the hegemony of our expensive friends who spend their lives digging deeper and deeper into the nucleus and the cosmos.” Don’t fret, he says reassuringly. More is different.

Writing

Anderson’s writings are not, however, limited to the technical papers and the occasional critique of reductionism. A wonderful and expansive collection of essays and reviews titled More and Different: Notes from a Thoughtful Curmudgeon, published in 2011, gives the reader a sense of the breadth of Anderson’s engagement with science, philosophy and politics. As an energetic participant in the ‘Science Wars’, Anderson was a strong critic of Republican administrations’ attitude towards scientific truths, and a frequent (and excellent) reviewer of books. Indeed, few scientists can match the breadth and clarity of Anderson’s writings.

He was in particular not afraid to call out the scientific establishment for its various flaws. Thoughtful meditations on the degree of independence experimental and theoretical work ought to have are accompanied by detailed discussions of scientific fraud. Broadsides against the rampant (as he saw it) unprofessionalism plaguing the high-temperature superconductivity community are just a few pages down from stinging critiques of the sociology of science. Many of these sociological issues, like self-aggrandisement and misleading press releases, are problems that still plague the practice of science today, and Anderson’s discussion is – once again – prescient.

A consistent thread across all his writings, however, is an effervescent optimism about the scientific possibilities that lay ahead, a certainty that explanations lay within our reach.

Sheldon Glashow once said of the late Sidney Coleman:

He was a giant in a peculiar sense, because he’s not known to the general populace… he has virtually no visibility outside. But within the community of theoretical physicists, he’s kind of a major god. He is the physicist’s physicist.

Much the same could be said of Philip Warren Anderson. However, it would be a mistake to see Anderson as just that. In the scientific establishment, we are taught to embrace an ever-narrowing disciplinary expertise as the sole arbiter of value in a researcher. To flirt with other fields is to risk becoming a dilettante, to invite scorn and criticisms of “not being serious.”

In Anderson, we are supplied with an example of a different kind of academic. One who is possessed of an inexhaustible curiosity for all branches of science, an ability to recognise common themes relating hitherto disparate fields, a willingness and enthusiasm to write in the popular scientific presses, and a critical attitude towards the sociological and political aspects of scientific life.

Anderson was much more than his contemporaries, and quite different.

Madhusudhan Raman is a postdoctoral fellow at the Tata Institute of Fundamental Research in Mumbai. The views expressed here are the author’s own.